Question: Which of the following numbers is a factor of 192? ${5,10,11,12,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $192$ by each of our answer choices. $192 \div 5 = 38\text{ R }2$ $192 \div 10 = 19\text{ R }2$ $192 \div 11 = 17\text{ R }5$ $192 \div 12 = 16$ $192 \div 13 = 14\text{ R }10$ The only answer choice that divides into $192$ with no remainder is $12$ $ 16$ $12$ $192$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $192$ $192 = 2\times2\times2\times2\times2\times2\times3 12 = 2\times2\times3$ Therefore the only factor of $192$ out of our choices is $12$. We can say that $192$ is divisible by $12$.